London has been battered by 50mph winds that have felled trees and caused travel chaos. Powerful gusts swept across the capital as the Met Office issued a yellow "be aware" weather alert for most of the country.

Londoners are bearing the brunt of benefit cuts with thousands losing more than £5,000-a-year amid growing signs of an exodus from the city centre.

More than 7,000 households in the capital are set to see welfare payments reduced by at least £100-a-week by the overall benefit cap of £26,000-a-year.

In Brent, 900 households will see such a drop, and 600 in both Westminster and Enfield.

Housing benefit has already been limited to £250-a-week for a one-bedroom property rising to £400 for a four-bedroom house.

The majority of the public, according to polls, support the caps.

The Government has stressed that many working families are unable to afford homes which unemployed people are living in on benefits.

The debate has been swayed by ministers highlighting the “absurd situation” where some families could claim £2,000-a-week to live in large houses in some of London’s most sought-after districts.

However, the capital is also seeing by far the most people affected by the caps, largely down to rents being so high.

The number of housing benefit claimants in private rented flats or houses in more central boroughs has fallen by more than 4,000 in the year to February 2013, including by nearly 2,000 in Westminster.

As some people have moved out of the city centre, the number of such claimants in outer London has risen by more than 5,000.

“There is growing evidence that the housing benefit cuts and high rents may be making large parts of inner London no-go areas for the working poor,” said London Assembly Green member Darren Johnson.

Sutton Council warned the “exodus” was creating new pressures for the capital’s leafy suburban districts, making it harder for local people to find schools, homes and health services.

“The historical patchwork of London’s housing supply, that saw the rich living cheek by jowl with the poor is now coming undone,” said Cllr Jayne McCoy, Chair of Sutton’s housing, economy and business committee.

Cllr Steve Curran, Hounslow’s cabinet member for housing, added: “Housing benefits changes are pushing more people out of central London and into boroughs like Hounslow, which is making it harder for people to find homes they can afford in their local community.”

No studies have yet shown how many people are leaving central London for outer suburbs or further afield, and Westminster denied “no-go areas” were being created.

Cllr Jonathan Glanz, Westminster’s Cabinet member for housing, said: “We are committed to creating and maintaining mixed communities and we, along with our housing associations have 24,000 social housing properties in Westminster.”

But Labour believes London should have a different overall cap than the regions.

Shadow employment minister Stephen Timms said the capital was being “punitively hit” by the £26,000 limit.

The Department for Work and Pensions stressed its reforms, including to incapacity payments, aimed to encourage people into work and has published figures suggesting that thousands of people have already moved off benefits into jobs.

A spokeswoman added: “The benefit cap sets a fair limit to what people can expect to get from the welfare system.”

Town halls had received £190 million in transitional funds to help those hardest hit by the housing benefit changes.

The DWP also emphasised that since the reforms were introduced, the number of housing benefit claimants living in the private rental sector in Greater London had risen by some five per cent.